Rashford thumped home the VAR-awarded spot-kick in the 94th minute after Diogo Dalot’s speculative shot struck Presnel Kimpembe on the arm.

The odds were stacked against United in Paris, but they became the first team in Champions League and European Cup history, at the 107th time of asking, to overcome a 2-0 or greater home first-leg deficit.

Ole Gunnar Solskjaer’s visitors got the perfect start thanks to Romelu Lukaku’s opportunist strike after two minutes, the Belgium striker latching on to Thilo Kehrer’s blind backpass and finding the net.

PSG went 3-1 ahead on aggregate when Kylian Mbappe fed a pass to the unmarked Juan Bernat, who slotted home at the back post.

The hosts then had a succession of chances, with makeshift right-back Eric Bailly enduring a torrid time in his 35 minutes on the pitch, before injury saw him replaced by Dalot.

Unable to capitalise, PSG were punished when veteran goalkeeper Gianluigi Buffon spilled Rashford’s long-range shot and Lukaku converted United’s second.

The game appeared to be petering out to its conclusion before Dalot fired the ball against the arm of the unfortunate Kimpembe, and after a long delay while the referee consulted his pitch-side monitor, Rashford’s ice-cool penalty sealed a remarkable win.

The draw for the quarter-finals takes place on Friday, 15 March.

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• Man Utd’s thrilling Paris finale in pictures

Incredible late drama in Paris

United were heading out at the last-16 stage for the second consecutive season when France defender Kimpembe’s block from Dalot’s shot deflected away for a corner.

But before it could be taken Slovenian referee Damir Skomina consulted with the VAR before coming to the side of the pitch to review the incident on the monitor.

Players waited anxiously on the pitch and Kimpembe slumped to the ground when the penalty was finally awarded, before Rashford stepped up to smash the ball high beyond the reach of Buffon.

United had to survive until the game’s 100th minute before joyously celebrating a famous Champions League victory in front of their boisterous travelling support at the final whistle.

• Relive an enthralling night of Champions League drama

Solskjaer’s side roll back the years

The result came 20 years on from United’s most memorable triumph when they claimed the treble of Premier League, FA Cup and Champions League, the latter after Solskjaer’s own injury-time winner in the final against Bayern Munich.

The Norwegian has overseen a remarkable turnaround which has seen the side collect 14 victories from 17 games in all competitions, including away wins at Tottenham, Arsenal, Chelsea and now PSG.

The former United striker has not only brought back the smiles to a side that was so abject before Christmas, but done so with outstanding tactical awareness and without the services of 10 first-team players.

Paul Pogba’s red card in the first leg meant he sat out the game alongside the nine injured players, so Bailly was given a start at right-back. However, the Ivorian turned in a wretched performance and was caught out of position time and time again.

An apparent injury to Bailly allowed Solskjaer to rectify this by bringing on Dalot and United looked much more solid thereafter.

Chris Smalling was superb at the back, contributing seven clearances and three interceptions alongside the unflappable Victor Lindelof, while midfielders Scott McTominay and Fred stood up magnificently against opposite numbers Marco Verratti and Marquinhos.

And up front, the often maligned Lukaku worked tirelessly and took his tally to 15 for the season with two well-taken finishes.

United have now won nine straight away games under Solskjaer and reached the last eight for the first time since 2014.

It now seems a case of when, not if, Solskjaer is named permanent manager.

PSG collapse in the last 16 – again

It was a familiar feeling for French powerhouses PSG, who may be 17 points clear at the top of their domestic league but once again demonstrated a lack of mental fortitude to see out a tie in which they were heavy favourites.

Only two seasons ago, they beat Barcelona 4-0 in the first leg at this same stage only to crumble to a 6-1 defeat in the second leg at the Nou Camp.

Wednesday’s result represents a first home defeat of the season for Thomas Tuchel’s side and ends their eight-game winning streak in all competitions.

At 3-2 up on aggregate, PSG laid siege to David de Gea’s goal but crucially spurned gilt-edged to kill the tie off. Dani Alves smashed over, Mbappe hit a shot into the side-netting, Bernat fired straight at De Gea and Angel di Maria drive flashed agonisingly wide, all before half-time.

United held their shape in the second half, having just 27.6% possession, and rode their luck when Bernat struck the foot of the post on 83 minutes.

Needing a goal, youth team player Tahith Chong was sent on for his first Champions League appearance and 17-year-old Mason Greenwood for his first-team debut, but it was another academy product in Rashford who stepped up to send them through, courtesy of VAR’s dramatic late intervention.

Super Solskjaer – the stats

• PSG conceded with three of the four shots on target they faced in this game and have been eliminated at the last 16 stage in each of the last three Champions League seasons.
• Romelu Lukaku’s first goal after 111 seconds was Man Utd’s fastest in a Champions League knockout match since Wayne Rooney scored after 63 seconds against Bayern Munich in March 2010.
• Since the start of last season, the only Premier League players to score more goals in all competitions than Man Utd’s Romelu Lukaku (42) are Mo Salah (64), Harry Kane (64) and Sergio Aguero (55).
• Marcus Rashford’s winning penalty was the first he has ever taken in a competitive match for Manchester United.
• PSG have lost seven of their last 12 Champions League knockout matches (W4 D1), including each of their last two at the Parc des Princes.
• Since Ole Gunnar Solskjaer’s first match in charge on 22 December, only Manchester City (15) have won more matches in all competitions than Man Utd (14) among teams in the top five European leagues.
• Manchester United have now scored in 21 consecutive away matches in all competitions, equalling the club record set between November 1956 and September 1957 under Sir Matt Busby.
• Mason Greenwood became the youngest player to appear for Manchester United in the Champions League, aged 17 years and 156 days, breaking the record held by Gerard Pique (17y 310d).